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All-Russian Olympiad
1990 All Soviet Union Mathematical Olympiad
523
ASU 523 All Soviet Union MO 1990 [n/1!] + [n/2!] + ... + [n/10!] = 1001
ASU 523 All Soviet Union MO 1990 [n/1!] + [n/2!] + ... + [n/10!] = 1001
Source:
August 14, 2019
floor function
diophantine
number theory
Problem Statement
Find all integers
n
n
n
such that
[
n
1
!
]
+
[
n
2
!
]
+
.
.
.
+
[
n
10
!
]
=
1001
\left[\frac{n}{1!}\right] + \left[\frac{n}{2!}\right] + ... + \left[\frac{n}{10!}\right] = 1001
[
1
!
n
]
+
[
2
!
n
]
+
...
+
[
10
!
n
]
=
1001
.
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